Optimization of the porous material described by the Biot model

Hübner, Daniel; Rohan, Eduard; Lukeš, Vladimír; Stingl, Michael

doi:10.1016/j.ijsolstr.2018.08.016

Cited by 10 publications

(13 citation statements)

References 27 publications

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“…In the further research, we intend to focus on the optimization of the peristaltic flow [4] by means of the microstructure design and the control. Also the self-contact at the pore level which would enable to minimize the fluid reflux and thus to enhance the pumping efficiency presents another challenging issue [11].…”

Section: Discussionmentioning

confidence: 99%

“…We present examples of microstructures and results of the simulations as the proof of concept aimed at designing smeared peristaltic pumps in a bulk medium. The computational tools are intended for subsequent two-scale design optimization [4] of local microstructures according to objectives of the macroscopic functionality, namely the fluid pumping.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale modelling of flow due to the peristaltic wave in deforming poro-piezoelectric medium

Rohan¹,

Lukeš²

2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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The paper reports on the homogenization based modelling of fluid saturated poroelastic materials containing locally controlable piezoelectric (PZ) actuators. This option provides metamaterial properties which enable to convert the electric power into the fluid transport due to the peristaltic deformation wave induced by the propagating voltage wave. A quasi-linear PZ-poroelastic material model is proposed to respect dependence of the effective medium parameters on the deformation at the microstructure (pore) level. Due to the sensitivity analysis of the homogenized coefficient, the two-scale modelling avoids any need to update the local microconfigurations. Numerical studies has been performed as the proof of the concept.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiscale modelling of flow due to the peristaltic wave in deforming poro-piezoelectric medium

Rohan¹,

Lukeš²

2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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“…Whereas, sensitivity analysis has been used in [3,17] to compute the derivatives with respect to the side lengths and the orientation of rectangular cavities. In [28], the derivatives with respect to the coefficients of a B-spline parametrization of the cavity have been computed. In [35], the shape derivative has been derived in the context of a level set representation of the inclusion.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric shape optimization for scaffold structures

Harbrecht¹,

Multerer²,

Rickenbach³

2021

Preprint

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The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape optimization and homogenization for the optimal design of the microstructure in scaffolds. Given the current microstructure, we apply the isogeometric boundary element method to compute the effective tensor and to update the microstructure by using the shape gradient in order to match the desired effective tensor. Extensive numerical studies are presented to demonstrate the applicability and feasibility of the approach.

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“…Typically problems are solved where the final design consist of a topology of fully permeable and impermeable material. For example, Guest and Prévost [7] coupled a fluid problem and topology optimization with a Darcy-Stokes approach and found out the optimal structure of porous media based on minimizing dissipated power; Shou and Fan [8] investigated the fast and controlled capillary flows in homogeneous porous structure and optimized the porous structure for imbibition of capillary flow with viscous resistance; Hübner et al [9] employed the Biot model for shape optimization of microstructure saturated viscous fluids and reported a two-scale structure of porous material based on effective poroelastic coefficients. However, to the best of our knowledge, multi-layer optimization of transient unsaturated flows in porous media has not been done before and is the main focus of our work.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of unsaturated flows in multi-material porous media: Application to a simple diaper model

Wein

Chen

Iqbal

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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We present a mathematical approach to optimize the material distribution for fluid transport in unsaturated porous media. Our benchmark problem is a simplified diaper model as an exemplary liquid absorber. Our model has up to three materials with vastly different properties, which in the reference configuration are arranged in parallel layers. Here, swelling is neglected and the geometry of a swollen diaper is assumed and treated as a porous medium of high porosity. The imbibition process is then simulated by solving an unsaturated flow problem based on Richards' equation. Our aim is to maximize the amount of absorbed liquid by redistributing the materials. To this end, a density based multi-material topology optimization (based on the well known SIMP model) is performed. A sensitivity analysis for the nonlinear transient problem is provided, which enables the application of first order optimization solvers. We perform two-and three-material optimization and discuss several variants of the problem setting. We present designs with up to 45% more absorbed liquid compared to the reference configuration.

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Optimization of the porous material described by the Biot model

Abstract: discussed. In order to avoid remeshing a geometric regularization technique based on injectivity constraints is applied.

Cited by 10 publications

References 27 publications

Multiscale modelling of flow due to the peristaltic wave in deforming poro-piezoelectric medium

Multiscale modelling of flow due to the peristaltic wave in deforming poro-piezoelectric medium

Isogeometric shape optimization for scaffold structures

Topology optimization of unsaturated flows in multi-material porous media: Application to a simple diaper model

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